And how much even simpler it would have been to define:

use constant BIT_0 => "\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\x01";
use constant BIT_1 => "\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\x02";
use constant BIT_2 => "\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\x04";
...
use constant BIT_127 => "\x80\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0";
...
my_subroutine(BIT_5 | BIT_8);
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and it just all works without requiring a new type or overloads. {grin}